Beyond Memorization: Using Ten-Frames to Build Number Sense
Do you ever feel that no matter how much you explain a concept, some students don’t seem to understand?
When this happens, I know I need to reevaluate my teaching approach. It usually means I need to include a visual illustration or representation for the concept I’m teaching.
In the past two years in my Waldorf classroom, I’ve started experimenting with ten-frames – a hands-on learning tool which is oh-so-helpful for my students in developing number sense.
Ten-frames have been a common learning resource for early math skills in non-Waldorf academic settings for many years. I have discovered that they can also be “Waldorfized” and woven beautifully into the math main lesson, enhancing number sense experiences for students, and ultimately, strengthening student understanding.
What is a Ten-Frame?
A ten-frame is a grid of 10 boxes, five in a row, doubled on top of each other. The boxes that are filled in represent the number. This ten-frame illustrates the number 10.
A ten-frame can help a child see what an abstract number symbol means.
Ten-frames can be used in many ways, including:
exploring parts of numbers
comparing numbers
understanding number patterns
working with math facts
Some options for using ten-frames include providing ready-made images that the students must evaluate, such as this one here. You could find these by exploring sources online.
I prefer, however, to provide each child with a blank grid and objects for them to fill in the grid according to the concepts we’re exploring in class.
I find it important for all students to create the visual representation with their own hands, rather than watching the teacher do it, or simply looking at a filled-in ten-frame.
In my class we use glass gems for counting objects. They fit perfectly into the ten-frame grids I provide, they are colorful, and the children like the smooth feel of them in their fingers.
How a Ten-Frame Can be Used in Different Grades
Ten-frames are so helpful for developing foundational number sense for our very youngest learners. But they can also be used with older learners and more complex number situations. Below are a few ways I have found ten-frames supportive in the Waldorf classroom.
First Grade
The ten-frame grid is a powerful visual tool for supporting object counting and relating the number of objects to their number symbols.
Starting with a single ten-frame and working with numbers within 10, the children can start with understanding what 5 looks like and then what 10 looks like.
From here they can begin to form number relationships in comparison to 5 or 10. This example shows that 6 is just one more than 5, and 7 is 2 more than 5.
Ten-frames support addition and subtraction facts.
One way to illustrate addition bonds is to use two separate colors of gems. The students can see the total number of gems, in this case, 10. The two parts are easily identified by color.
From there they can independently write the number sentence: 6 + 4 = 10, or 10 = 6 + 4.
Subtraction is a concept my students have found more challenging than addition when facing it purely in number form. Somehow, 10-3 is harder for them than 3+7. The ten-frame offers the perfect visual representation for them to see the inter-relatedness of addition and subtraction.
Starting with a frame filled with 10, the students can pull outside of the frame the number being subtracted. This leaves a very easy visual picture for the remaining amount.
Of course, the next step is to write the number sentence: 10 - 3 =7.
Once first graders are confident with numbers within 10, they are ready for two ten-frames, and now can gain a deeper understanding of the teens.
The teens do not convey the place value of 10 in their name, as the rest of the two-digit numbers do. So it is important for children to see that each of the teens is a full 10 with the ones value added on in the next frame.
Here students can experience 12 as 10 and 2.
The numbers 11, 12, 13, and 15 do not even contain the name of the ones value, so the children need to see what these numbers look like and then relate the visual representation to the number symbols.
Second Grade
Two-digit Numbers
Ten-frames are also a wonderful tool for place-value concepts and counting by 10s. When I dictate a large number (below 100), the children enthusiastically fill many frames in with gems, allowing any leftovers to be in a separate frame to compose the ones value. They then write the number, linking the abstract symbol to their ten-frame count.
Adding two double-digit numbers also works well with ten-frames in a partner activity. I assign each child a different number to compose, and then they must combine them using addition, sometimes requiring them to “carry” 10 extra gems into a completely new ten-frame. This is a great precursor for vertical addition, which I wait to introduce as an algorithm until third grade.
Third Grade
As we learn our multiplication families from memory in second and third grade, we’re preparing to isolate the individual multiplication facts later on in third and then fourth grade. A ten-frame can be used to illustrate the groupings that multiplication represents. We ask the students to memorize a fact like 8 x 3, but it’s hard to remember what that means visually, even if it was taught back in first grade.
Ten-frames offer the visual and hands-on experience of the groupings, which multiplication represents. Here they can see that we have 3 in a group 8 times (8 x 3). If they have been practicing their skip counting for the 3s family, they can easily count up to the total number of gems.
Once the students click with this visual, they can more easily use their own strategies to calculate the answers of their multiplication facts, ultimately leading to memorization.
Experiment and Observe
I hope that you will decide to explore using ten-frames, and give it some time to feel comfortable in your daily rhythm! To make it easier for you to implement, I’m including the link below to my ten-frame templates. You can download, print, and photocopy these as many times as you would like for use with your students. On the link, you will find a large single ten-frame, and two smaller double ten-frames. I also included two colors . . . dark green and black. Just click the link below.
Each of the examples above is just that . . . an example of what has worked for me with my students that you, too, could try out.
But, the options are really endless. The important thing is to try out some of these activities, observe how the students engage and respond, and reflect upon your own systems of delivery and presentation.
If at first these ten-frames seem challenging to implement, don’t give up! Anything that is new takes time to develop and learn, and that goes for us as teachers, too!
The main thing to keep in mind is to allow the students to explore and come up with their own strategies for solving the problems you give them. It’s okay for them to struggle a little bit. You can model a way for thinking that works for you, but then allow them to experiment and explore.
And, finally, allow time at the end of your lesson to inquire about their thinking, giving time for different students to explain how they came up with their answers. It can be helpful and inspiring to classmates to hear other ways of thinking.
Free Ten-Frame Template for You to Download
My students absolutely love working with ten-frames and gems during math blocks. I hope you find inspiration in exploring ways to incorporate ten-frames into your classroom so that your students can love working with them as well! Below is the link for you to download my ten-frame templates so you can use them, too. Enjoy!
